WASHINGTON (CNN) -- U.S. Sen. David Vitter returned from a week-long absence from Congress Tuesday, a day after he made a public apology for "a serious sin" as investigators probe an alleged prostitution ring that operated in the nation's capital.

Vitter vanished from public view last week after his phone number turned up among those kept by a reputed "D.C. Madam" in records that have become part of her upcoming criminal trial.

The Louisiana conservative apologized privately to his fellow Republican senators at their weekly policy lunch Tuesday, senators who attended the lunch said.

Tuesday morning, Vitter did not visit his Senate office, where the media had camped out in anticipation of his return. He also was not seen at a residential address near the Supreme Court building.

He eventually emerged at a scheduled Senate hearing taking place near his office building. He arrived nearly 30 minutes late for the start of the panel, which heard testimony regarding commercial airline service to outlying parts of the United States.

At first, only CNN and a local camera crew had learned of his whereabouts. But as word spread among media outlets, Senate officials had to urge order among the gaggle of newspaper writers, photographers and other television crews that began making noisy entrances to record Vitter's return.

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The senator left the hearing early and tried to ignore shouted questions and camera lights in the hallway. He then turned and stopped.

Vitter referred to comments he made Monday evening near New Orleans, Louisiana, then said, "I look forward today to be back at work, really focused on a lot of important issues for the people of Louisiana. I'll leave it at that."

Last week, Vitter acknowledged in a statement that his number had turned up in the telephone records of accused "D.C. Madam" Deborah Jeane Palfrey. Vitter, 46, said those calls were made prior to his election to the Senate in 2004, and he and his wife had already dealt with what he termed a "serious sin" privately, through marriage counseling and confession to a Roman Catholic priest.

On Monday, Vitter and his wife Wendy spoke to reporters in the New Orleans suburb of Metairie, where he lives. "I know this has hurt the relationship of trust I've enjoyed with so many of you and that I have a lot of work to do to rebuild that trust," the senator said.

Palfrey is facing money laundering and racketeering charges stemming from her alleged prostitution operation. She had denied the charges, saying her business was a legitimate, legal escort service. At first she tried to sell the phone records to raise money for her defense.

After a judge imposed restrictions on the records, Palfrey distributed the records without charge, hoping media outlets would help track down clients who her lawyer believes may help in her defense.

Vitter is the first lawmaker entangled in the case, although State Department official Randall Tobias resigned in May after confirming he patronized Palfrey's business.

Larry Flynt's Hustler magazine claimed credit for exposing Vitter's connection to Palfrey, saying he came clean only after a journalist working as a paid consultant for the magazine discovered the senator's number in her phone records.E-mail to a friend